Could the deployment of self-driving cars make rides free?
You ask an interesting question.  There have been many discussions by industry on this topic.  A company called Vugo has their business model based on advertising to passengers.  An article about Vugo, "The Quest to Make Ridesharing Free", states:


Flessner is co-founder and CEO of Minneapolis-based rideshare advertising platform Vugo, which uses its patented TripIntent technology to display targeted advertisements to Uber and Lyft passengers on a tablet attached to the back of the vehicle’s headrests.
The company’s founders predict that within the next few years, all ridesharing vehicles in the U.S. will be driverless, and in-vehicle advertising tailored to passengers’ destinations and interests will lead to free transportation. “The idea is to put brands in front of passengers who are en route to make purchases,” says Flessner. For example, retailers will sponsor transportation to their stores so they can preview products to customers who are headed their way.


This article "How free self-driving car rides could change everything" makes these comments:


Car data is so lucrative that Ben Volkow -- CEO of otonomo, an Israeli startup that sells vehicle data -- expects automakers to make more money selling data than vehicles by 2020.
If the money made off self-driving vehicle data outweighs the costs of offering rides, then it becomes reasonable for a business to offer free rides broadly.


A paper entitled "Leveraging Adverts in the Coming
Autonomous Car Eco-system" published by Berkeley, University of California, proposes "a world where rideshares are free, or in some cases, heavily subsidized through the use of advertisements".